The topic of this paper is the analysis of a recently developed numerical method for the
approximate calculation of fractional derivatives [1]}. Specifically, we assume a function
\(y \in C^{\lceil \alpha \rceil }[a, a+T]\)  to be given with some \(T > 0\)  and some \(a \in \mathbb {R}\) ,
and the task is to compute the Caputo derivative \(D_a^\alpha y(t_j)\)  of order \(\alpha \in \mathbb {R}_+ \setminus \mathbb {N}\) 
of the function \(y\)  [2]} at some points \(t_0 < t_1 < t_2 < \cdots < t_N\) 
with \(t_0 =a\)  and \(t_N = a+T\)  being the two end points of the interval of interest.
The algorithm is based on the diffusive representation
\(D_a^\alpha y(t) = \int _{-\infty }^\infty \phi _{\mathrm {D}}(w, t) \mathrm {d} w\) 
